83.8.18 problem 19

Internal problem ID [19073]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 19
Date solved : Monday, March 31, 2025 at 06:43:31 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right )&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 25

ode:=2*y(x)+3*x*diff(y(x),x)+2*x*y(x)*(3*y(x)+4*x*diff(y(x),x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_1 +\ln \left (1+2 \textit {\_Z} \right )+3 \ln \left (\textit {\_Z} \right )\right )}{x} \]

✓ Mathematica. Time used: 60.248 (sec). Leaf size: 1565

ode=2*y[x]+3*x*D[y[x],x]+2*x*y[x]*(3*y[x]+4*x*D[y[x],x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*(4*x*Derivative(y(x), x) + 3*y(x))*y(x) + 3*x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out